Question: Solve for $x$ and $y$ using elimination. ${6x+y = 68}$ ${5x-y = 42}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $11x = 110$ $\dfrac{11x}{{11}} = \dfrac{110}{{11}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {6x+y = 68}\thinspace$ to find $y$ ${6}{(10)}{ + y = 68}$ $60+y = 68$ $60{-60} + y = 68{-60}$ ${y = 8}$ You can also plug ${x = 10}$ into $\thinspace {5x-y = 42}\thinspace$ and get the same answer for $y$ : ${5}{(10)}{ - y = 42}$ ${y = 8}$